a^2+9a=-20

Solution for a^2+9a=-20 equation:

Simplifying
a2 + 9a = -20

Reorder the terms:
9a + a2 = -20

Solving
9a + a2 = -20

Solving for variable 'a'.

Reorder the terms:
20 + 9a + a2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 9a + a2 = 0

Factor a trinomial.
(5 + a)(4 + a) = 0

Subproblem 1
Set the factor '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + a = 0 + -5
a = 0 + -5

Combine like terms: 0 + -5 = -5
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Solution
a = {-5, -4}